具有指数记忆的离散分数阶微积分:命题、数值格式和渐近稳定性

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Modelling and Control Pub Date : 2023-11-07 DOI:10.15388/amc.2024.29.33550

Guang Yang, Guo-Cheng Wu, Hui Fu

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引用次数: 0

摘要

提出了一种新的带指数核函数的分数阶差分。首先，用指数函数定义一个差分算子。从n阶差分方程的柯西问题出发，提出了新的分数阶和与差。推导了它们之间的命题和数值格式。最后，给出了分数阶线性差分方程，并利用一种新的离散Mittag-Leffler函数给出了精确解。

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Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability

A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.